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Can help me how to factorise this

http://prntscr.com/b0ol03

The numerator I can do but I can't do the denominator when they add the 2 to the x^2 i get confused and have no idea how to do it. Can anyone explain to me how to do.

Thanks
Reply 1
Avatar for nao123
nao123
7
what 2 numbers multiply to give -30 and add to give -7?
Factorise 2x2−7x−152x^2-7x-15.

Need two numbers whose product is a∗c=2∗−15=−30a*c = 2*-15=-30 and sum is b=−7b= -7 (from ax^2+bx+c).
−10-10 and +3+3 will work.

Split the 'x' term up (put the -10x first since you can factorise it with the 2x^2 as you will see)

2x2−10x+3x−152x^2-10x+3x-15
=2x(x−5)+3(x−5)=2x(x-5)+3(x-5)
=(2x+3)(x−5)=(2x+3)(x-5)
Reply 3
Avatar for Zacken
Zacken
22
Hint: −30=3×−10-30 = 3 \times -10

Edit: bleh, ignore this - listen to notnek.
(edited 7 years ago)
Reply 4
Avatar for Notnek
Notnek
21
Original post by junayd1998
http://prntscr.com/b0ol03

The numerator I can do but I can't do the denominator when they add the 2 to the x^2 i get confused and have no idea how to do it. Can anyone explain to me how to do.

Thanks

The previous posters are using the 'ac' method. Ignore that for now if you've never used it before.


Your bracket look okay so far.

So you need two numbers that multiply to give -15. There aren't too many combinations. Try some numbers then expand the brackets to check they work.

If you're stuck, tell us what you've tried.
2x^2 - 7x - 15 = (2x + 3) (x -5)
Reply 6
Avatar for Notnek
Notnek
21
Original post by AdRiAnRsT
2x^2 - 7x - 15 = (2x + 3) (x -5)

:sigh:
Reply 7
Avatar for C-rated
C-rated
2
I usually just do the quadratic formula and times one of the results by two and see if it works when put back into the formula, if it doesn't then I times the other by two x)

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